A method and system for quickly obtaining the time-delay stability region of a power system based on critical ride-through

Abstract

The present invention discloses a method and system for quickly obtaining a time-delay stability domain of an electric power system based on critical crossing, comprising: establishing a characteristic quasi-polynomial model of a periodic time-delay electric power system based on two characteristics of crossing frequency and critical time lag; estimating a value set of the periodic characteristic quasi-polynomial model according to Taylor transform and Bernstein transform; determining a stable boundary on the FDM space by performing zero-removal discrimination on the periodic characteristic quasi-polynomial value set and splitting the FDM space; obtaining a stable boundary on the time-delay space based on the stable boundary mapping on the FDM space, and determining a stable domain. Based on the simplicity and smoothness of the stable boundary on the FDM space, the present invention can realize a fast search for the stable boundary.

Description

Technical Field

[0001] The present invention relates to the technical field of power system time-delay stability domain calculation, and in particular to a method and system for quickly obtaining a power system time-delay stability domain based on critical crossing. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] In recent years, with the establishment of modern large-scale interconnected power grids, the network structure and dynamic behavior of power systems have become more complex, and the use of wide-area measurement technology for management and control has become a necessary measure. However, there is a significant delay in wide-area measurement information, which seriously affects various stability analyses and controller effects of power systems.

[0004] The time lag effect exists not only in large power grids, but also in microgrids. As an efficient and flexible way of utilizing energy, microgrids are the best solution to solve the power supply problem in areas that cannot be reached by large power grids. With the continuous development of microgrids, considering the randomness and intermittency of renewable energy output and the volatility of loads, global control is required, which requires the introduction of communication networks to transmit data and issue control instructions.

[0005] When there is a non-negligible time delay in the signal transmission process, the microgrid becomes a typical delayed cyber-physics power system (DCPPS). The time delay effect may cause the theoretically well-designed controller to perform poorly or even fail, making it difficult to meet the requirements of safe operation of the power grid.

[0006] Therefore, it is very necessary to conduct in-depth research on the time-delay-related stability analysis of power systems and find the time-delay range that enables the system to remain stable, which will play a positive role in ensuring the stable operation of the system and the optimal design of the coordinated controller.

[0007] At present, there are two main methods for studying the stability of time-delay systems: the time domain method and the frequency domain method. The time domain method mainly constructs the time-delay-dependent stability criterion based on the Lyapunov-Krasovskii and Razumikhin theorems, and with the help of the linear matrix inequality (LMI) technology, it can easily obtain the system's time-delay margin under the premise of ensuring asymptotic stability. However, the time-delay-dependent stability criterion is a sufficient condition for the stability of the system under small disturbances, and it is somewhat conservative; and it can only obtain the system's time-delay margin, and cannot obtain the time-delay stability domain when the time delay changes over a large range.

[0008] The frequency domain method is mainly based on characteristic analysis. When the rightmost eigenvalue of the system is on the imaginary axis, the system is in a critical stability state. The frequency domain method can be roughly divided into three categories: 1) Rekasius transform method, which uses Rekasius transform to eliminate the time-delay transcendental term and transform the time-delay system into a time-delay-free system to analyze the stability of small disturbances; 2) Eigenvalue algorithm, which sets a suitable step size, scans the time-delay space and calculates the eigenvalue to obtain the time-delay stability domain. However, space scanning will lead to a large amount of calculation; 3) Value set method, which does not use the traditional way of solving eigenvalues, but is based on the principle of zero removal, and analyzes stability by judging whether the characteristic quasi-polynomial value set of the system contains zero points. The value set method is a general method that can not only be used to analyze the impact of parameter uncertainty on system stability in traditional time-delay-free power systems, but also can be used to study the stability of small disturbances of systems considering time-delay uncertainty, and can handle multiple time delays at the same time.

[0009] However, most of the existing methods are only effective when the time delay is small. When the system time delay is large due to blockage or interference in the communication loop, it is necessary to study the topological structure and boundary properties of the stable domain of the power system in a large range of time delay space. At this time, the above methods are not competent. Summary of the invention

[0010] In order to solve the above problems, the present invention proposes a method and system for quickly obtaining the time-delay stability domain of an electric power system based on critical crossing, which utilizes the periodicity of the transcendental terms of the characteristic quasi-polynomial of the time-delay electric power system at the critical stability point to quickly search for the time-delay range that ensures the stability of the electric power system with small disturbances.

[0011] In some embodiments, the following technical solutions are adopted:

[0012] A method for quickly obtaining the time-delay stability region of a power system based on critical ride-through includes:

[0013] Based on the two characteristics of cross-frequency and critical time delay, a characteristic quasi-polynomial model of power system with periodic time delay is established.

[0014] Estimate the value set of the periodic characteristic quasi-polynomial model based on Taylor and Bernstein transforms;

[0015] By removing zero from the periodic characteristic quasi-polynomial value set and splitting the FDM space, the stable boundary on the FDM space is determined;

[0016] Based on the stable boundary mapping in FDM space, the stable boundary in the time-delay space is obtained and the stable domain is determined.

[0017] In other embodiments, the following technical solutions are adopted:

[0018] A system for rapidly obtaining time-delay stability region of a power system based on critical ride-through, comprising:

[0019] A model building module is used to build a periodic characteristic quasi-polynomial model based on the crossover frequency and critical time lag characteristics;

[0020] A value set estimation module, used for estimating the value set of its Taylor model according to the established periodic characteristic quasi-polynomial model;

[0021] A stable boundary determination module is used to determine the stable boundary by performing zero elimination judgment on the value set estimation result of the characteristic quasi-polynomial Taylor model and splitting the FDM space;

[0022] The stable domain obtaining module is used to obtain the stable boundary and stable domain in the time-delay space according to the stable boundary mapping in the FDM space.

[0023] In other embodiments, the following technical solutions are adopted:

[0024] A non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the above-mentioned method for quickly obtaining the time-delay stability domain of an electric power system based on critical crossing is implemented.

[0025] In other embodiments, the following technical solutions are adopted:

[0026] An electronic device comprises: a processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes the above-mentioned method for quickly obtaining the time-delay stability domain of an electric power system based on critical crossing.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1) Based on the two characteristics of crossing frequency and critical time lag, the present invention proposes a periodic translation method for solving the stability boundary in the time lag space and FDM space; based on the simplicity and smoothness of the stability boundary in the FDM space, a fast search for the stability boundary can be achieved; the periodic application of the characteristic quasi-polynomial at critical stability can achieve the expansion of the stability boundary from only one period to any range in the time lag space; the application of the value set method and zero rejection can ensure the accuracy of the stability boundary result.

[0029] Other features and advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a flow chart of a method for determining a stable boundary in an FDM space in an embodiment of the present invention;

[0031] Figure 2 Flow chart of a mapping method for determining a stable boundary and a stable domain in a time-delay space in an embodiment of the present invention;

[0032] Figure 3 Schematic diagram of crossover frequency and critical time lag characteristics in an embodiment of the present invention;

[0033] Figure 4 It is a schematic diagram of the stability boundary result of a first-order time-delay system in the time-delay space in an embodiment of the present invention;

[0034] Figure 5 It is a schematic diagram of the stability boundary result of the first-order time-delay system in the FDM space in an embodiment of the present invention;

[0035] Figure 6 Schematic diagram of the stability boundary results of a first-order time-delay system in different ranges in the time-delay space in an embodiment of the present invention;

[0036] Figure 7 A single-line diagram of the centralized microgrid line parameters and network structure in an embodiment of the present invention;

[0037] Figure 8 It is a schematic diagram of the calculation result of the small disturbance time-delay stability domain of the centralized microgrid in an embodiment of the present invention;

[0038] Fig. 9 It is a schematic diagram of a small disturbance time-delay stability domain result obtained by traversing the time-delay space to solve the eigenvalue of the centralized microgrid in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0040] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0041] Embodiment 1

[0042] In one or more embodiments, a method for quickly obtaining the time-delay stability domain of an electric power system based on critical crossing is disclosed. The method is based on the idea that the characteristic quasi-polynomial of the electric power system has periodicity at the critical stability point, considers the impact of large-scale communication delays caused by channel blocking and other reasons, and determines the large-scale time-delay stability domain that ensures the small-disturbance stability of the electric power system from a periodic analysis.

[0043] The principle and derivation process of the method of this embodiment are as follows:

[0044] Assuming that the system has m uncertain time delays, the linearized model of the power system and its corresponding characteristic quasi-polynomial can be expressed as:

[0045]

[0046]

[0047] In the formula, is the linearized state vector; is the state matrix, i=0,1,…,m; τ is the time delay vector,

[0048] The purpose of this embodiment is to use the value set of the characteristic quasi-polynomial of formula (2) to determine the critical time lag Make the eigenvalue of the system lie on the imaginary axis Ω=(-∞,+∞).

[0049]

[0050] In the formula, the binary The element ω c and Represent the set of all crossover frequencies and the set of all critical time delays respectively. The corresponding set of curves (m=2), surfaces (m=3) or hypersurfaces (m>3) on the time-delay space T is the time-delay stability boundary.

[0051] The stability boundary in the time-delay space is very complex, and it is very time-consuming to determine the stability boundary directly in the time-delay space. Moreover, when the time-delay range considered is too large due to reasons such as channel blocking, the amount of calculation to determine the stability boundary of a large range of time-delays will show an approximately exponential growth trend.

[0052] In order to solve these two existing technical problems, the characteristics of crossing frequency and critical time lag can be used to process the characteristic quasi-polynomial. Starting from the periodicity of the characteristic quasi-polynomial at the critical stable point, the stable boundary and stable domain can be quickly analyzed and solved.

[0053] The method for quickly obtaining the time-delay stability region of a power system based on critical ride-through in this embodiment specifically includes the following process:

[0054] Step (1): Based on the two characteristics of crossover frequency and critical time delay, a characteristic quasi-polynomial model of the power system with periodic time delay is established;

[0055] In this embodiment, a periodic vector is constructed on the FDM space based on the crossover frequency and critical time-delay characteristics; and the characteristic quasi-polynomial of the periodic time-delay power system is obtained by substitution using the periodic vector on the FDM space.

[0056] Specifically, the crossover frequency and critical time delay of the time-delay power system shown in equation (1) have the following two unique properties.

[0057] 1) For all possible time delays There are only a finite number (K) of frequencies Passing through the imaginary axis;

[0058] 2) For each crossover frequency There are infinitely many critical time delays with periodic intervals in, is the minimum positive lag vector, that is Can be used to represent the residual time lag vector

[0059]

[0060] in,

[0061] By multiplying both sides of equation (4) by the crossover frequency, we can get a sequence with a period of 2π. Obviously, the product of the crossover frequency and the critical time lag has a constant period.

[0062]

[0063] To take advantage of the periodicity, the product of the frequency and the time delay vector is defined as a new vector Among them, ε i =ωτ i , i=1,2,…,m is located in the frequency-delay product FDM space and is expressed as By replacing the variables in equation (2), we can establish the imaginary axis Characteristic quasi-polynomial model with 2π period on .

[0064]

[0065] To facilitate the subsequent description, the imaginary axis The characteristic quasi-polynomial f(jω,ε) on the simplifies to f(x), x=[x1,x2,…,x s ]T ∈X, where represents the uncertainty space. The corresponding characteristic quasi-polynomial value set is f(X) = {f(x)|x∈X}.

[0066] Step (2): Estimate the value set of the periodic characteristic quasi-polynomial model according to Taylor transform and Bernstein transform;

[0067] In this embodiment, a Taylor model of periodic characteristic quasi-polynomial is established;

[0068] The Bernstein transformation is performed on the polynomial part of the Taylor model of the characteristic quasi-polynomial, and the inner and outer estimates of the characteristic quasi-polynomial value set are solved using the convex combination of Bernstein coefficients.

[0069] Specifically, the characteristic quasi-polynomial f(x) of the time-delay power system contains exponential terms and cannot be approximated as an affine uncertain structure, so it is impossible to quickly construct a value set using the edge theorem and mapping theorem. In order to eliminate the influence of the exponential terms, f(x) is approximated as a Taylor model T(f(x)) = p(u) + R(X) consisting of a polynomial p(u) and a remainder interval R(X) through Taylor transformation, where is the normalized value of x.

[0070] Then the polynomial part of the characteristic quasi-polynomial Taylor model T(f(x)) is transformed by Bernstein.

[0071]

[0072] In the formula, is the Bernstein basis function. is the Bernstein coefficient.

[0073] The convex combination of Bernstein coefficients can be used to quickly solve the inner and outer estimates of the characteristic quasi-polynomial value set. The specific process is divided into two steps:

[0074] 1) Solve the outer estimate of the characteristic quasi-polynomial value set. First, the outer estimate P of the Taylor model polynomial partial value set P(U) ex (U) can be represented by the convex hull of the Bernstein coefficients. Then, the remainder interval R(X) is added to P ex At each point of (U), a remainder band R is formed ex . The remainder is R ex The outer contour is the outer estimate of the characteristic quasi-polynomial F ex (X).

[0075] 2) Solve the internal estimate of the characteristic quasi-polynomial value set. First, the internal estimate P of the polynomial value set P(U) in (U) can be determined by the edges E on space U i (i=s·2s-1 )'s external estimate P(E i ) is represented by the inner area enclosed by i ) can also be expressed as i The convex hull of the corresponding Bernstein coefficients, i = 1, 2, ..., s 2 s-1 Then, add the remainder interval R(X) to P in At each point of (U), a remainder band R is formed in . The remainder is R in The inner contour of is the inner estimate of the characteristic quasi-polynomial F in (X).

[0076] Step (3): Determine the stable boundary on the FDM space by performing zero removal on the periodic characteristic quasi-polynomial value set and splitting the FDM space;

[0077] In this embodiment, the inner and outer estimates of the estimated characteristic quasi-polynomial Taylor model are subjected to zero removal discrimination; the FDM space is split based on the zero removal discrimination result, and a stable boundary on the FDM space is obtained by selective splitting during the process of traversing the FDM space.

[0078] Specifically, the exact value set of the characteristic quasi-polynomial of the time-delay power system must be located between the inner and outer estimates of the characteristic quasi-polynomial value set. Based on the generalization of the following zero-removal principle in the time-delay system, the zero-removal judgment is performed by judging the zero point and the inner estimate F of the characteristic quasi-polynomial value set. in (X), external estimate F ex (X) to analyze the stability of the uncertain space X;

[0079] Extension of the zero-elimination principle: The characteristic quasi-polynomial f(λ,ε) of a time-delay system is robustly stable for all uncertain variables ε∈E if and only if: ① There exists a set of variables ε (i) ∈E, so that the real part of all eigenvalues ​​of the system is less than 0; ② For all ω ≥ 0, there is

[0080] If the zero point is located outside the estimated F ex (X), then the exact value set definitely excludes the zero point, and the system is absolutely stable; if the zero point is located within the estimated F in (X), then the exact value set must contain zero, and the system is absolutely unstable; if the zero is between the inner and outer estimates, the relationship between the exact value set and the zero cannot be determined, that is, the stability cannot be determined. It is inevitable to split the uncertainty space X to make the inner and outer estimates closer to the exact value set.

[0081] If the zero point is between the inner and outer estimates, it is necessary to select the splitting dimension of the uncertainty space X according to different principles. If the zero point is on the remainder band, the main reason why stability is difficult to judge is that the range of high-order remainders retained during Taylor transformation is too large. Therefore, it is necessary to select the dimension with the largest average norm of the remainder interval as the splitting dimension according to the principle of minimizing the remainder interval in order to achieve the purpose of rapid judgment.

[0082]

[0083] Otherwise, the main reason why stability is difficult to judge is that the accuracy of using the Bernstein coefficient to estimate the p(u) value set of the polynomial part of the Taylor model is insufficient. Therefore, it is necessary to select the dimension with the largest first-order partial derivative of p(u) as the splitting dimension based on the principle of the most accurate polynomial value set estimation to achieve the purpose of quick judgment.

[0084] The first-order partial derivative of the polynomial p(u) in the r-th dimension is:

[0085]

[0086] in, is a first-order difference operator.

[0087] Furthermore, the maximum first-order partial derivative of the polynomial p(u) can be estimated as Right now:

[0088]

[0089] Based on the above ideas, a process of determining the stable boundary of FDM space by splitting and traversing the uncertain space based on the result of zero removal is summarized, as follows: Figure 1 As shown. Since the stability boundary on the FDM space is periodic, it is only necessary to obtain the system in [0,2π] m If we find a stable boundary within (a subset of the entire FDM space), we can easily use equation (5) to construct the stable boundary of the entire FDM space.

[0090] Step (4): Based on the stable boundary mapping in the FDM space, the stable boundary in the time-delay space is obtained, and the stable domain is determined.

[0091] In this embodiment, the relationship between the periodic vector in the FDM space and the time-delay vector and the crossing frequency is utilized, and the stable boundary in the time-delay space is obtained by mapping the stable boundary in the FDM space. Fixed time-delay points are selected in each time-delay region divided by the stable boundary to calculate the eigenvalues ​​and determine the time-delay stability domain.

[0092] Specifically, using the obtained stable boundary and corresponding crossover frequency in the FDM space, the relationship between the variables in the FDM space and the time-delay variables εi =ωτ i ,i=1,2,…,m, through the inverse transformation, the stable boundary in the large-scale time-delay space can be obtained, and then the stable domain can be determined. The process of solving the stable boundary and stable domain in the time-delay space is as follows Figure 2 In this process, the stability of the region is determined by selecting a fixed time-delay point on the region divided by the time-delay stability boundary and solving the eigenvalue, thereby determining the stability domain of the entire time-delay space.

[0093] In each divided area, a time-delay point is selected to solve the eigenvalue. This is the problem of solving the eigenvalue of the time-delay system (the method for this problem is already very mature, such as EIGD). If all the eigenvalues ​​are located on the left half-complex plane, the system is stable at the time-delay point, and then it can be determined that the time-delay area is stable. The reason why the stability of a time-delay point can be used instead of the stability of a region is that the time-delay space is divided into multiple regions by the stability boundary, and the number of eigenvalues ​​of the system corresponding to each region located on the right half-complex plane is fixed (because the situation where the eigenvalue crosses the imaginary axis only occurs on the time-delay stability boundary).

[0094] In this embodiment, the number of times the uncertain space is split has the greatest impact on the amount of calculation. Since the stable boundary in the FDM space is periodic, the graphics in each period will not overlap, and the graphics are simple and smooth, so the number of cycles in the space splitting link will be greatly reduced. Compared with the direct study in the time-delay space, the amount of calculation is effectively reduced.

[0095] This embodiment can quickly determine the stability of the system in the current uncertain space by selectively determining the dimension of space splitting, and can effectively optimize the number of times of space splitting to minimize it, thereby further improving the efficiency of the method.

[0096] Since the periodicity of the characteristic quasi-polynomial at the critical stable point is fully utilized, by modifying l in formula (5), the initial period [0,2π] m The stable boundary on the whole space is obtained by translating the stable boundary on the whole space. The amount of calculation does not increase with the increase of the spatial range, which ensures the scalability of the method.

[0097] Embodiment 2

[0098] This embodiment uses a first-order system with two uncertain time delays as an example to illustrate how to use the crossover frequency and critical time delay characteristics to quickly construct a stable boundary. By comparing it with directly calculating the stable boundary in the time delay space, it shows the beneficial effect of the method of mapping the stable boundary in the FDM space to obtain the stable boundary in the time delay space in terms of efficiency.

[0099] The characteristic quasi-polynomial model of the time-delay system in this embodiment is as follows:

[0100]

[0101] The crossover frequency and critical time delay characteristics of system (11) can be obtained by Figure 3 For explanation. Figure 3 In the current crossing frequency Next, critical lag Located in the kth slice, where is the lower left point. Based on the periodicity in formula (4), we determine This can be done by using a grid size of 2π / ω c The periodic translation of automatically forms other critical time-delay points on the kth slice. The sum of all critical time-delay points on each slice constitutes the time-delay stability boundary of the system, such as Figure 4 shown.

[0102] If Figure 3 The kth slice in the equation is multiplied by the current crossing frequency Then, by summing, we can obtain the ratio in the frequency-delay product (FDM) space. Figure 4 A simpler and smoother stable boundary in Figure 5 Based on the periodicity in formula (5), it is determined that the entire stable boundary in the FDM space can be determined by the initial period [0,2π] in the lower left corner. 2 The stable boundary on is obtained by periodic translation, and the grid size of the translation is constant at 2π.

[0103] In the lower left of FDM space [0,2π] 2 The calculation of the stable boundary within the range can be implemented according to steps 1 to 3 in the technical solution of embodiment 1. First, the periodic characteristic quasi-polynomial model of the embodiment system is established by step 1, as follows:

[0104]

[0105] If the angular frequency range is set to ω∈[0,20]rad / s, the uncertainty space is X=E1×E2×Ω=[0,2π]×[0,2π]×[0,20]. The corresponding characteristic quasi-polynomial is abbreviated as f(x)(x=[x1,x2,x3]∈X}.

[0106] Then, the internal and external estimates of the f(x) value set are quickly constructed, and the internal and external estimates of the obtained value set are removed by zero discrimination. By splitting and traversing the uncertainty space X, the [0,2π] in the FDM space is determined. 2The stable boundary in the range is obtained, and then the stable boundary in the entire FDM space can be obtained by periodic translation. The stable boundary in the time-delay space can be obtained by indirect mapping from the stable boundary in the FDM space. The number of times the system (12) of this embodiment splits the uncertain space is 8528 times, and the total calculation time is 2.1s.

[0107] If the method of directly calculating the stability boundary in the time-delay space is adopted, the time-delay stability boundary is calculated in the range of 0~3s, 0~5s and 0~8s respectively. The results are as follows Figure 6 As shown in (a)-(c) in the figure, the corresponding number of space splits is 18144, 75683 and 277677 times, and the total calculation time is 22.3s, 124.1s and 439.4s, respectively. It can be observed that with the increase of the time lag range, the time lag stability boundary curve becomes more complex, which directly leads to a rapid increase in the number of space splits, and then a rapid increase in the calculation time.

[0108] Comparing the results of the two methods, it is demonstrated that the method of indirectly mapping the stable boundary in the FDM space to the stable boundary in the time-delay space has a beneficial effect on computational efficiency, and the calculation time is almost unaffected by the range of the time-delay.

[0109] Embodiment 3

[0110] In this embodiment, a microgrid under centralized control is taken as an example to illustrate how to determine the small disturbance stability domain of an actual multi-time-delay power system in the time-delay space, and at the same time demonstrates the beneficial effect of the method of the present invention in terms of accuracy.

[0111] The microgrid structure and line parameters described in this embodiment are as follows: Figure 7 As shown in the figure, it consists of three inverters with a rated capacity of 10kVA each, with two load groups. The loads of 5.8kW, 5.8kVar (=24Ω, 18.5mH / phase) at bus 1 and 7.3kW, 7.3kVar (=20Ω, 23.2mH / phase) at bus 2 are taken as the initial working points. Under the centralized control mode, each DG communicates bidirectionally with the upper central controller, and the communication delays of the three DGs are τ1, τ2 and τ3 respectively.

[0112] Similarly, the angular frequency range is set to ω∈[0,20]rad / s. Then, the stability boundary and stability domain of the system in the time-delay space are calculated according to the steps in the technical scheme of Example 1. Among them, steps (1) to (3) can refer to the specific description of the first-order system example in Example 2. The mapping to obtain the stability boundary and stability domain in the time-delay space is based on solving the stability boundary in the FDM space. Through formula (5), the stability boundary in the time-delay space is mapped by the stability boundary in the FDM space and the cross-frequency corresponding to each critical stability point.

[0113] Furthermore, the characteristics of each region divided by the time-delay stability boundary in the time-delay space are analyzed to determine the stability domain. The results are as follows: Figure 8 As shown in (a), if the time delay τ2 = 54ms is considered, the stability domain on the τ1×τ3 plane is as follows: Figure 8 As shown in (b).

[0114] If the eigenvalue algorithm is used, the time-delay stability domain is obtained by setting an appropriate step size (here set to 0.01), scanning the time-delay space and calculating the eigenvalue. The result is as follows Fig. 9 The gray area is shown, where the black solid line is Figure 8 The time-delay stability boundary obtained by the method of the present invention in (b) is shown in Figure 1. It can be observed that the results obtained by the two methods are consistent, demonstrating the beneficial effect of the method of the present invention in terms of accuracy.

[0115] Embodiment 4

[0116] In one or more embodiments, a system for quickly obtaining a time-delay stability region of a power system based on critical ride-through is disclosed, comprising:

[0117] A model building module is used to build a periodic characteristic quasi-polynomial model based on the crossover frequency and critical time lag characteristics;

[0118] A value set estimation module, used for estimating the value set of its Taylor model according to the established periodic characteristic quasi-polynomial model;

[0119] A stable boundary determination module is used to determine the stable boundary by performing zero elimination judgment on the value set estimation result of the characteristic quasi-polynomial Taylor model and splitting the FDM space;

[0120] The stable domain obtaining module is used to obtain the stable boundary and stable domain in the time-delay space according to the stable boundary mapping in the FDM space.

[0121] It should be noted that the specific implementation methods of the above modules have been described in Example 1 and will not be described in detail here.

[0122] Embodiment 5

[0123] An embodiment of the present invention provides a non-transitory computer-readable storage medium, which is used to store computer instructions. When the computer instructions are executed by a processor, a method for quickly obtaining a small disturbance stability domain of a time-delay power system based on critical crossing characteristics described in Example 1 is implemented.

[0124] Embodiment 6

[0125] An embodiment of the present invention provides an electronic device, comprising: a processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the method for quickly obtaining the small disturbance stability domain of a time-delay power system based on the critical crossing characteristics described in Example 1.

[0126] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for quickly obtaining the time-delay stability region of a power system based on critical ride-through, characterized in that: include: Based on the two characteristics of crossover frequency and critical time delay, a characteristic quasi-polynomial model of a periodic time-delay power system is established, which specifically includes: constructing a periodic vector on the FDM space based on the crossover frequency and critical time delay characteristics; using the periodic vector on the FDM space to replace the characteristic quasi-polynomial of the periodic time-delay power system; Define the product of the frequency and the time delay vector as a new vector A characteristic quasi-polynomial model with a 2π period is established, specifically: Where ω is the angular frequency range, ε i =ωτ i , i = 1, 2, ..., m, located in the frequency-delay product FDM space, expressed as Estimate the value set of the periodic characteristic quasi-polynomial model based on Taylor and Bernstein transforms; By performing zero-elimination on the periodic characteristic quasi-polynomial value set and splitting the FDM space, the stable boundary on the FDM space is determined, specifically including: performing zero-elimination on the inner and outer estimates of the estimated characteristic quasi-polynomial Taylor model; splitting the FDM space based on the zero-elimination result, and obtaining the stable boundary on the FDM space through selective splitting in the process of traversing the FDM space; Based on the stable boundary mapping on the FDM space, the stable boundary on the time-delay space is obtained, and the stable domain is determined, which specifically includes: utilizing the relationship between the periodic vector on the FDM space and the time-delay vector and the crossing frequency, obtaining the stable boundary on the time-delay space by the stable boundary mapping on the FDM space, and selecting fixed time-delay points on each time-delay area divided by the stable boundary to calculate the eigenvalue to determine the time-delay stable domain.

2. A method for rapidly obtaining the time-delay stability region of a power system based on critical ride-through according to claim 1, characterized in that: The value set of the periodic characteristic quasi-polynomial model is estimated based on Taylor transform and Bernstein transform, specifically including: Establish Taylor model of periodic characteristic quasi-polynomial; The Bernstein transformation is performed on the polynomial part of the Taylor model of the characteristic quasi-polynomial, and the inner and outer estimates of the characteristic quasi-polynomial value set are solved using the convex combination of Bernstein coefficients.

3. A method for rapidly obtaining the time-delay stability region of a power system based on critical ride-through according to claim 2, characterized in that: The outer estimate of the characteristic quasi-polynomial value set is specifically: The outer estimate of the partial value set of Taylor model polynomial is expressed by the convex hull of Bernstein coefficients; Add the remainder interval to each point of the outer estimate of the partial value set to form a remainder band; The outer contour of the remainder band is the outer estimate of the characteristic quasi-polynomial.

4. A method for rapidly obtaining a time-delay stability region of a power system based on critical ride-through according to claim 2, characterized in that: The inner estimation of the characteristic quasi-polynomial value set is specifically: The inner estimate of the polynomial value set is represented by the inner region enclosed by the outer estimates of the edges on the space U; The remainder interval is added to each point of the inner estimate of the polynomial value set to form a remainder band; the inner contour of the remainder band is the inner estimate of the characteristic quasi-polynomial.

5. A system for rapidly obtaining the time-delay stability region of a power system based on critical ride-through, characterized in that: include: The model building module is used to establish a periodic characteristic quasi-polynomial model based on the cross-over frequency and critical time-delay characteristics, specifically including: constructing a periodic vector on the FDM space based on the cross-over frequency and critical time-delay characteristics; using the periodic vector on the FDM space to replace to obtain the characteristic quasi-polynomial of the periodic time-delay power system; Define the product of the frequency and the time delay vector as a new vector A characteristic quasi-polynomial model with a 2π period is established, specifically: Where ω is the angular frequency range, ε i =ωτ i , i = 1, 2, ..., m, located in the frequency-delay product FDM space, expressed as A value set estimation module, used for estimating the value set of its Taylor model according to the established periodic characteristic quasi-polynomial model; The stable boundary determination module is used to determine the stable boundary by performing zero-elimination judgment on the value set estimation result of the characteristic quasi-polynomial Taylor model and splitting the FDM space, specifically including: performing zero-elimination judgment on the inner and outer estimates of the estimated characteristic quasi-polynomial Taylor model; splitting the FDM space based on the zero-elimination judgment result, and obtaining the stable boundary on the FDM space by selectively splitting in the process of traversing the FDM space; The stable domain obtaining module is used to obtain the stable boundary and stable domain in the time-delay space according to the stable boundary mapping in the FDM space, specifically including: utilizing the relationship between the periodic vector in the FDM space and the time-delay vector and the crossing frequency, obtaining the stable boundary in the time-delay space by the stable boundary mapping in the FDM space, and selecting fixed time-delay points in each time-delay area divided by the stable boundary to calculate the eigenvalue to determine the time-delay stable domain.

6. A non-transitory computer-readable storage medium for storing computer instructions, characterized in that: When the computer instructions are executed by the processor, the method for quickly obtaining the time-delay stability region of a power system based on critical crossing as described in any one of claims 1 to 4 is implemented.

7. An electronic device comprising: A processor, a memory and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory, and is characterized in that when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes the method for quickly obtaining the time-delay stability domain of the power system based on critical crossing as described in any one of claims 1-4.

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